TSTP Solution File: LCL151-1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LCL151-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:11:44 EDT 2023
% Result : Unsatisfiable 278.27s 37.14s
% Output : CNFRefutation 278.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 7
% Syntax : Number of clauses : 215 ( 215 unt; 0 nHn; 10 RR)
% Number of literals : 215 ( 214 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 507 ( 78 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(big_V_definition,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',big_V_definition) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',wajsberg_1) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',wajsberg_4) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',wajsberg_3) ).
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',wajsberg_2) ).
cnf(big_hat_definition,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',big_hat_definition) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
big_V(big_hat(x,y),z) != big_hat(big_V(x,z),big_V(y,z)),
file('/export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p',prove_wajsberg_theorem) ).
cnf(c_0_7,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
big_V_definition ).
cnf(c_0_8,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_9,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_10,plain,
implies(X1,X1) = big_V(truth,X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_12,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_13,plain,
implies(big_V(truth,not(X1)),big_V(truth,X1)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
big_V(X1,X2) = big_V(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_7]),c_0_7]) ).
cnf(c_0_15,plain,
implies(X1,big_V(X1,X2)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_8]),c_0_8]),c_0_7]) ).
cnf(c_0_16,plain,
implies(big_V(truth,not(X1)),big_V(X1,truth)) = truth,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
big_V(truth,X1) = truth,
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_18,plain,
big_V(X1,truth) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_8]) ).
cnf(c_0_19,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_20,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_19]),c_0_8]),c_0_8]) ).
cnf(c_0_21,plain,
big_V(X1,implies(X2,X1)) = implies(big_V(X2,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_14]) ).
cnf(c_0_22,plain,
implies(implies(big_V(X1,X2),X3),implies(X1,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_8]) ).
cnf(c_0_23,plain,
implies(X1,big_V(X2,X1)) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_24,plain,
implies(big_V(X1,X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_20]),c_0_8]),c_0_21]) ).
cnf(c_0_25,plain,
implies(big_V(truth,X1),X1) = big_V(X1,X1),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_26,plain,
implies(X1,big_V(X2,big_V(X1,X3))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_8]) ).
cnf(c_0_27,plain,
big_V(X1,implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_28,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_29,axiom,
big_hat(X1,X2) = not(big_V(not(X1),not(X2))),
big_hat_definition ).
cnf(c_0_30,plain,
big_V(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_17]),c_0_8]) ).
cnf(c_0_31,plain,
implies(X1,big_V(X2,implies(X3,X1))) = truth,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
big_V(X1,implies(not(X1),not(truth))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_28]),c_0_8]),c_0_14]) ).
cnf(c_0_33,plain,
big_V(not(truth),not(not(truth))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_28]),c_0_14]) ).
cnf(c_0_34,plain,
not(not(X1)) = big_hat(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
implies(not(truth),X1) = truth,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
implies(big_V(X1,X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_37,plain,
big_V(big_hat(truth,truth),not(truth)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_14]) ).
cnf(c_0_38,plain,
big_V(not(truth),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_35]),c_0_8]) ).
cnf(c_0_39,plain,
implies(not(truth),big_hat(truth,truth)) = big_hat(truth,truth),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_8]) ).
cnf(c_0_40,plain,
implies(implies(not(X1),not(implies(X2,X1))),big_V(X2,X1)) = truth,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_41,plain,
big_V(X1,not(truth)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_42,plain,
big_hat(truth,truth) = truth,
inference(rw,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_43,plain,
implies(not(implies(X1,not(truth))),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]),c_0_42]),c_0_8]) ).
cnf(c_0_44,plain,
implies(X1,implies(not(X1),not(truth))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_43]),c_0_8]) ).
cnf(c_0_45,plain,
implies(not(X1),not(truth)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_44]),c_0_8]),c_0_32]) ).
cnf(c_0_46,plain,
implies(X1,not(truth)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_45]),c_0_41]) ).
cnf(c_0_47,plain,
not(not(X1)) = big_hat(truth,X1),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_48,plain,
big_hat(X1,big_V(not(X2),not(X3))) = not(big_V(not(X1),big_hat(X2,X3))),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_49,plain,
big_hat(truth,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,plain,
big_V(not(X1),not(X2)) = not(big_hat(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_38]) ).
cnf(c_0_51,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_52,plain,
implies(not(big_V(X1,X2)),not(X1)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_46]) ).
cnf(c_0_53,plain,
not(big_hat(X1,not(X2))) = big_V(not(X1),X2),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
implies(big_hat(X1,X2),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_47]),c_0_49]),c_0_47]),c_0_49]) ).
cnf(c_0_55,plain,
big_V(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_12]),c_0_8]) ).
cnf(c_0_56,plain,
big_V(implies(X1,X2),implies(not(X2),not(X1))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_8]),c_0_14]) ).
cnf(c_0_57,plain,
not(big_V(not(X1),X2)) = big_hat(X1,not(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_58,plain,
big_V(X1,big_hat(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_54]),c_0_8]),c_0_14]) ).
cnf(c_0_59,plain,
not(big_hat(not(X1),X2)) = big_V(X1,not(X2)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
implies(X1,big_V(big_V(X1,X2),X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_8]) ).
cnf(c_0_61,plain,
big_V(X1,big_V(X2,X1)) = big_V(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_8]) ).
cnf(c_0_62,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_46]),c_0_56]),c_0_46]) ).
cnf(c_0_63,plain,
implies(not(X1),implies(X1,X2)) = truth,
inference(spm,[status(thm)],[c_0_31,c_0_56]) ).
cnf(c_0_64,plain,
big_hat(X1,big_V(X1,not(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_47]),c_0_49]),c_0_59]) ).
cnf(c_0_65,plain,
implies(X1,big_V(big_V(X2,X1),X3)) = truth,
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
implies(implies(X1,X2),not(X1)) = not(big_hat(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_62]),c_0_50]) ).
cnf(c_0_67,plain,
big_V(not(X1),implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_63]),c_0_8]) ).
cnf(c_0_68,plain,
big_hat(X1,big_V(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_69,plain,
big_V(X1,big_V(big_V(X2,X1),X3)) = big_V(big_V(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_65]),c_0_8]) ).
cnf(c_0_70,plain,
implies(implies(X1,implies(X2,X3)),implies(big_V(X2,X3),implies(X1,X3))) = truth,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_71,plain,
implies(X1,implies(not(X1),X2)) = truth,
inference(spm,[status(thm)],[c_0_63,c_0_51]) ).
cnf(c_0_72,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_73,plain,
implies(X1,big_hat(X2,X1)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_66]),c_0_62]),c_0_14]),c_0_67]) ).
cnf(c_0_74,plain,
big_hat(X1,X2) = big_hat(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_29]) ).
cnf(c_0_75,plain,
big_hat(X1,big_V(big_V(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,plain,
implies(big_V(not(X1),X2),implies(X1,X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_8]) ).
cnf(c_0_77,plain,
implies(X1,not(implies(X1,X2))) = not(big_hat(X2,X1)),
inference(rw,[status(thm)],[c_0_66,c_0_72]) ).
cnf(c_0_78,plain,
implies(X1,big_hat(X1,X2)) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
big_hat(X1,implies(X2,big_V(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_27]) ).
cnf(c_0_80,plain,
big_V(X1,big_hat(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_74]) ).
cnf(c_0_81,plain,
implies(implies(implies(X1,X2),X3),implies(implies(X3,X2),big_V(X1,X2))) = truth,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_82,plain,
implies(big_hat(X1,X2),big_hat(X2,implies(X2,X1))) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_50]),c_0_62]) ).
cnf(c_0_83,plain,
implies(implies(X1,X2),big_hat(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_78]),c_0_58]) ).
cnf(c_0_84,plain,
big_hat(big_hat(X1,X2),implies(X3,X2)) = big_hat(X1,X2),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
implies(big_V(X1,X2),big_V(big_V(X1,X3),X2)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_22]),c_0_7]),c_0_8]) ).
cnf(c_0_86,plain,
big_V(big_V(not(X1),X2),not(X3)) = not(big_hat(big_hat(X1,not(X2)),X3)),
inference(spm,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_87,plain,
big_V(implies(X1,X2),implies(implies(big_hat(X2,X1),X3),implies(X1,X3))) = implies(implies(big_hat(X2,X1),X3),implies(X1,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_73]) ).
cnf(c_0_88,plain,
implies(big_hat(X1,X2),big_hat(X1,implies(X1,X2))) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_74]) ).
cnf(c_0_89,plain,
big_V(implies(X1,X2),implies(X1,big_hat(X2,X3))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_8]),c_0_8]),c_0_14]) ).
cnf(c_0_90,plain,
implies(big_hat(big_hat(X1,not(X2)),X3),big_hat(X1,X3)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_50]),c_0_62]) ).
cnf(c_0_91,plain,
implies(big_hat(X1,X2),X2) = truth,
inference(spm,[status(thm)],[c_0_54,c_0_74]) ).
cnf(c_0_92,plain,
implies(X1,big_hat(X2,implies(X2,X1))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_8]),c_0_89]),c_0_8]) ).
cnf(c_0_93,plain,
big_V(implies(X1,X2),implies(implies(big_hat(X1,X2),X3),implies(X1,X3))) = implies(implies(big_hat(X1,X2),X3),implies(X1,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_78]) ).
cnf(c_0_94,plain,
implies(big_hat(big_hat(X1,X2),X3),big_hat(X1,X3)) = truth,
inference(spm,[status(thm)],[c_0_90,c_0_51]) ).
cnf(c_0_95,plain,
big_V(implies(X1,X2),implies(X1,big_hat(X3,X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_91]),c_0_8]),c_0_8]),c_0_14]) ).
cnf(c_0_96,plain,
not(big_hat(X1,big_hat(X2,implies(X2,X1)))) = not(big_hat(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_92]),c_0_77]),c_0_74]) ).
cnf(c_0_97,plain,
implies(big_hat(X1,X2),big_hat(X1,X3)) = implies(big_hat(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_8]),c_0_95]),c_0_8]) ).
cnf(c_0_98,plain,
big_hat(X1,big_hat(X2,implies(X2,X1))) = big_hat(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_96]),c_0_51]) ).
cnf(c_0_99,plain,
implies(big_hat(X1,X2),big_hat(X2,X3)) = implies(big_hat(X1,X2),X3),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_100,plain,
implies(not(X1),big_hat(X2,not(X3))) = implies(big_V(not(X2),X3),X1),
inference(spm,[status(thm)],[c_0_62,c_0_57]) ).
cnf(c_0_101,plain,
implies(X1,big_hat(big_V(X1,X2),X3)) = implies(X1,X3),
inference(spm,[status(thm)],[c_0_99,c_0_68]) ).
cnf(c_0_102,plain,
implies(big_V(big_hat(X1,not(X2)),X3),X1) = implies(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_62]),c_0_57]) ).
cnf(c_0_103,plain,
implies(big_V(big_hat(X1,X2),X3),X1) = implies(X3,X1),
inference(spm,[status(thm)],[c_0_102,c_0_51]) ).
cnf(c_0_104,plain,
implies(big_V(big_hat(X1,X2),X3),X2) = implies(X3,X2),
inference(spm,[status(thm)],[c_0_103,c_0_98]) ).
cnf(c_0_105,plain,
implies(big_V(X1,big_hat(X2,X3)),X3) = implies(X1,X3),
inference(spm,[status(thm)],[c_0_104,c_0_14]) ).
cnf(c_0_106,plain,
big_hat(X1,big_V(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_61]) ).
cnf(c_0_107,plain,
big_hat(not(X1),not(X2)) = not(big_V(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_51]) ).
cnf(c_0_108,plain,
implies(big_V(X1,X2),big_V(X3,X2)) = implies(X1,big_V(X3,X2)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,plain,
implies(X1,implies(X2,big_V(X1,X3))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_8]) ).
cnf(c_0_110,plain,
implies(big_V(X1,X2),not(implies(X2,X1))) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_107]),c_0_62]),c_0_72]) ).
cnf(c_0_111,plain,
implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,big_V(X1,X2))) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_7]),c_0_108]) ).
cnf(c_0_112,plain,
big_V(implies(X1,big_V(X2,X3)),implies(implies(X2,X3),implies(X1,X3))) = implies(implies(X2,X3),implies(X1,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_113,plain,
implies(X1,implies(X2,big_V(X3,X1))) = truth,
inference(spm,[status(thm)],[c_0_109,c_0_61]) ).
cnf(c_0_114,plain,
not(implies(implies(X1,X2),implies(X3,X2))) = not(implies(X3,big_V(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_46]),c_0_112]) ).
cnf(c_0_115,plain,
big_hat(not(X1),implies(X1,X2)) = not(X1),
inference(spm,[status(thm)],[c_0_68,c_0_67]) ).
cnf(c_0_116,plain,
implies(big_hat(X1,X2),implies(X3,X1)) = truth,
inference(spm,[status(thm)],[c_0_113,c_0_58]) ).
cnf(c_0_117,plain,
big_hat(X1,implies(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_27]) ).
cnf(c_0_118,plain,
implies(big_hat(X1,X2),big_hat(X3,X1)) = implies(big_hat(X1,X2),X3),
inference(spm,[status(thm)],[c_0_97,c_0_74]) ).
cnf(c_0_119,plain,
big_hat(X1,not(implies(X1,X2))) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_67]) ).
cnf(c_0_120,plain,
implies(implies(X1,X2),implies(X3,X2)) = implies(X3,big_V(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_114]),c_0_51]) ).
cnf(c_0_121,plain,
implies(implies(X1,X2),big_hat(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_66]),c_0_62]),c_0_115]),c_0_47]),c_0_49]) ).
cnf(c_0_122,plain,
big_V(big_hat(X1,X2),implies(X3,X1)) = implies(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_116]),c_0_8]) ).
cnf(c_0_123,plain,
implies(big_V(X1,X2),implies(X3,X2)) = implies(X1,implies(X3,X2)),
inference(spm,[status(thm)],[c_0_105,c_0_117]) ).
cnf(c_0_124,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_125,plain,
implies(not(implies(X1,X2)),big_hat(X3,X1)) = implies(not(implies(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_126,plain,
implies(X1,implies(X2,big_hat(X3,X1))) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_14]),c_0_122]) ).
cnf(c_0_127,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_7]),c_0_123]),c_0_14]),c_0_21]),c_0_24]) ).
cnf(c_0_128,plain,
implies(not(big_hat(X1,X2)),implies(X2,X3)) = implies(not(implies(X2,X3)),X1),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,plain,
implies(X1,implies(not(big_hat(X2,X1)),X3)) = implies(not(X3),implies(X1,X2)),
inference(spm,[status(thm)],[c_0_126,c_0_124]) ).
cnf(c_0_130,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)),
inference(spm,[status(thm)],[c_0_124,c_0_127]) ).
cnf(c_0_131,plain,
implies(not(X1),implies(X2,X3)) = implies(X2,implies(not(X3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_127]),c_0_129]),c_0_130]) ).
cnf(c_0_132,plain,
implies(implies(not(X1),X2),implies(X3,X1)) = implies(X3,big_V(not(X2),X1)),
inference(spm,[status(thm)],[c_0_120,c_0_124]) ).
cnf(c_0_133,plain,
implies(not(X1),big_V(not(X2),X3)) = implies(big_hat(X2,not(X3)),X1),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_134,plain,
implies(big_hat(implies(X1,X2),not(X3)),X2) = big_V(X1,implies(not(X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_131]),c_0_132]),c_0_133]) ).
cnf(c_0_135,plain,
implies(big_hat(implies(X1,X2),X3),X2) = big_V(X1,implies(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_51]),c_0_62]) ).
cnf(c_0_136,plain,
implies(big_V(X1,implies(X2,X3)),X3) = big_V(X3,big_hat(implies(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_135]),c_0_14]) ).
cnf(c_0_137,plain,
implies(X1,big_V(X2,big_V(X3,X1))) = truth,
inference(spm,[status(thm)],[c_0_26,c_0_61]) ).
cnf(c_0_138,plain,
implies(big_V(implies(X1,X2),X3),X2) = big_V(X2,big_hat(implies(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_136,c_0_14]) ).
cnf(c_0_139,plain,
big_V(implies(X1,X2),implies(X3,X2)) = implies(big_hat(big_V(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_135,c_0_7]) ).
cnf(c_0_140,plain,
implies(big_hat(X1,X2),big_V(X3,X1)) = truth,
inference(spm,[status(thm)],[c_0_137,c_0_58]) ).
cnf(c_0_141,plain,
big_V(X1,big_hat(big_V(X2,X1),X3)) = big_V(X1,big_hat(big_V(X3,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_7]),c_0_7]),c_0_14]) ).
cnf(c_0_142,plain,
big_V(X1,big_V(big_hat(X1,X2),X3)) = big_V(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_103]),c_0_7]),c_0_14]) ).
cnf(c_0_143,plain,
implies(big_hat(big_hat(X1,X2),X3),X2) = truth,
inference(spm,[status(thm)],[c_0_140,c_0_80]) ).
cnf(c_0_144,plain,
big_V(X1,big_hat(big_V(X2,X1),X3)) = big_V(X1,big_hat(X2,big_V(X3,X1))),
inference(spm,[status(thm)],[c_0_141,c_0_74]) ).
cnf(c_0_145,plain,
big_V(X1,big_V(big_hat(X2,X1),X3)) = big_V(X3,X1),
inference(spm,[status(thm)],[c_0_142,c_0_98]) ).
cnf(c_0_146,plain,
big_V(X1,big_hat(big_hat(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_143]),c_0_8]),c_0_14]) ).
cnf(c_0_147,plain,
big_hat(X1,big_hat(X2,X1)) = big_hat(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_80]),c_0_74]) ).
cnf(c_0_148,plain,
implies(big_V(X1,X2),implies(implies(X2,X3),implies(implies(X1,X2),X3))) = truth,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_149,plain,
implies(big_hat(X1,not(X2)),not(X3)) = implies(X3,big_V(not(X1),X2)),
inference(spm,[status(thm)],[c_0_62,c_0_57]) ).
cnf(c_0_150,plain,
implies(big_hat(big_V(X1,X2),X3),X2) = implies(big_hat(X1,big_V(X3,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_144]),c_0_36]) ).
cnf(c_0_151,plain,
not(big_V(X1,not(X2))) = big_hat(not(X1),X2),
inference(spm,[status(thm)],[c_0_51,c_0_59]) ).
cnf(c_0_152,plain,
implies(big_V(X1,X2),big_V(X1,X3)) = implies(X2,big_V(X1,X3)),
inference(spm,[status(thm)],[c_0_104,c_0_68]) ).
cnf(c_0_153,plain,
big_V(big_V(X1,X2),big_V(X1,X3)) = big_V(X3,big_V(X1,X2)),
inference(spm,[status(thm)],[c_0_145,c_0_68]) ).
cnf(c_0_154,plain,
big_V(X1,big_hat(X2,big_hat(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_155,plain,
implies(big_V(X1,X2),big_V(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_121]),c_0_78]),c_0_7]) ).
cnf(c_0_156,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_8]) ).
cnf(c_0_157,plain,
implies(X1,big_V(big_hat(not(X2),X1),X3)) = implies(X1,big_V(not(X2),big_hat(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_48]),c_0_57]),c_0_149]),c_0_151]) ).
cnf(c_0_158,plain,
implies(big_hat(X1,X2),implies(X3,X2)) = truth,
inference(spm,[status(thm)],[c_0_113,c_0_80]) ).
cnf(c_0_159,plain,
implies(implies(not(X1),X2),X1) = big_V(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_53]) ).
cnf(c_0_160,plain,
implies(big_V(X1,X2),big_V(X3,X1)) = implies(X2,big_V(X3,X1)),
inference(spm,[status(thm)],[c_0_104,c_0_106]) ).
cnf(c_0_161,plain,
big_V(X1,big_V(X2,X3)) = big_V(X3,big_V(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_152]),c_0_7]),c_0_153]) ).
cnf(c_0_162,plain,
big_V(X1,big_V(X2,big_V(X1,X3))) = big_V(X2,big_V(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_26]),c_0_8]) ).
cnf(c_0_163,plain,
big_V(big_V(X1,X2),big_hat(X3,X1)) = big_V(X1,X2),
inference(spm,[status(thm)],[c_0_154,c_0_68]) ).
cnf(c_0_164,plain,
big_V(big_V(X1,X2),big_V(X2,X1)) = big_V(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_155]),c_0_8]) ).
cnf(c_0_165,plain,
implies(big_V(X1,X2),big_V(implies(X3,X1),X2)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_156]),c_0_7]),c_0_8]) ).
cnf(c_0_166,plain,
implies(X1,big_V(big_hat(X2,X1),X3)) = implies(X1,big_V(X2,big_hat(X3,X1))),
inference(spm,[status(thm)],[c_0_157,c_0_51]) ).
cnf(c_0_167,plain,
big_V(big_hat(X1,X2),implies(X3,X2)) = implies(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_158]),c_0_8]) ).
cnf(c_0_168,plain,
big_V(implies(not(X1),X2),implies(X3,X1)) = implies(big_hat(not(X2),big_V(X3,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_159]),c_0_150]) ).
cnf(c_0_169,plain,
big_V(X1,big_V(X2,X3)) = big_V(X3,big_V(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_160]),c_0_7]),c_0_161]),c_0_162]) ).
cnf(c_0_170,plain,
big_V(big_V(X1,X2),big_hat(X3,big_V(X2,X1))) = big_V(X1,X2),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_171,plain,
big_V(big_V(X1,X2),X3) = big_V(X2,big_V(X1,X3)),
inference(spm,[status(thm)],[c_0_14,c_0_161]) ).
cnf(c_0_172,plain,
big_hat(big_V(X1,X2),big_V(implies(X3,X1),X2)) = big_V(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_165]),c_0_8]) ).
cnf(c_0_173,plain,
not(big_hat(X1,big_V(big_hat(X2,X1),X3))) = not(big_hat(X1,big_V(X2,big_hat(X3,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_166]),c_0_77]),c_0_74]),c_0_74]) ).
cnf(c_0_174,plain,
implies(X1,implies(X2,big_hat(X1,X3))) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_83]),c_0_14]),c_0_167]) ).
cnf(c_0_175,plain,
big_V(implies(X1,X2),implies(X1,X3)) = implies(X1,big_V(X2,big_hat(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_62]),c_0_47]),c_0_49]),c_0_50]),c_0_107]),c_0_62]) ).
cnf(c_0_176,plain,
implies(big_V(X1,big_V(X2,X3)),X2) = implies(big_V(X3,X1),X2),
inference(spm,[status(thm)],[c_0_36,c_0_169]) ).
cnf(c_0_177,plain,
big_V(X1,big_V(X2,big_hat(X3,big_V(X1,X2)))) = big_V(X2,X1),
inference(rw,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_178,plain,
big_V(implies(X1,X2),implies(X3,X2)) = implies(big_hat(X1,big_V(X3,X2)),X2),
inference(rw,[status(thm)],[c_0_139,c_0_150]) ).
cnf(c_0_179,plain,
big_hat(big_V(X1,X2),big_V(big_hat(X3,X1),X2)) = big_V(big_hat(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_121]),c_0_74]) ).
cnf(c_0_180,plain,
big_hat(X1,big_V(big_hat(X2,X1),X3)) = big_hat(X1,big_V(X2,big_hat(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_173]),c_0_51]) ).
cnf(c_0_181,plain,
implies(X1,implies(implies(X1,X2),X3)) = implies(big_hat(X2,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_77]),c_0_51]),c_0_62]) ).
cnf(c_0_182,plain,
implies(X1,implies(X2,not(implies(X1,X3)))) = implies(X2,not(big_hat(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_119]),c_0_77]) ).
cnf(c_0_183,plain,
implies(not(implies(X1,X2)),X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_67]),c_0_47]),c_0_49]) ).
cnf(c_0_184,plain,
big_hat(not(X1),big_V(X2,not(X3))) = not(big_V(X1,big_hat(not(X2),X3))),
inference(spm,[status(thm)],[c_0_151,c_0_151]) ).
cnf(c_0_185,plain,
big_V(implies(X1,X2),implies(big_V(X1,X2),X3)) = implies(X1,big_V(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_24]),c_0_106]),c_0_108]),c_0_14]) ).
cnf(c_0_186,plain,
implies(big_V(X1,big_hat(X2,big_V(X1,X3))),X3) = implies(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_36]),c_0_14]) ).
cnf(c_0_187,plain,
implies(X1,big_hat(X2,big_V(X1,X3))) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_101,c_0_74]) ).
cnf(c_0_188,plain,
implies(X1,big_V(X2,big_hat(X3,big_V(X1,X2)))) = implies(X1,big_V(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_178]),c_0_120]),c_0_120]),c_0_14]) ).
cnf(c_0_189,plain,
big_hat(X1,big_V(X2,big_hat(X3,X1))) = big_V(big_hat(X2,X1),big_hat(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_80]),c_0_180]),c_0_74]),c_0_147]) ).
cnf(c_0_190,plain,
implies(implies(X1,X2),not(big_hat(X3,X1))) = implies(big_hat(X2,X1),not(implies(X1,X3))),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_191,plain,
big_hat(X1,big_V(X2,big_V(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_61]) ).
cnf(c_0_192,plain,
big_V(X1,not(implies(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_183]),c_0_8]),c_0_14]) ).
cnf(c_0_193,plain,
implies(big_V(X1,X2),implies(X3,X1)) = implies(X2,implies(X3,X1)),
inference(spm,[status(thm)],[c_0_104,c_0_117]) ).
cnf(c_0_194,plain,
big_V(implies(X1,X2),implies(X3,not(X1))) = implies(X1,big_V(X2,big_hat(not(X3),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_62]),c_0_184]),c_0_62]) ).
cnf(c_0_195,plain,
implies(X1,big_V(X2,big_hat(X3,X1))) = implies(X1,big_V(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_187]),c_0_175]),c_0_188]) ).
cnf(c_0_196,negated_conjecture,
big_V(big_hat(x,y),z) != big_hat(big_V(x,z),big_V(y,z)),
prove_wajsberg_theorem ).
cnf(c_0_197,plain,
big_hat(X1,big_V(big_hat(X2,X1),X3)) = big_V(big_hat(X2,X1),big_hat(X3,X1)),
inference(rw,[status(thm)],[c_0_180,c_0_189]) ).
cnf(c_0_198,plain,
implies(implies(X1,X2),not(big_hat(X1,X3))) = implies(big_hat(X2,X1),not(implies(X1,X3))),
inference(spm,[status(thm)],[c_0_190,c_0_74]) ).
cnf(c_0_199,plain,
implies(big_hat(big_V(X1,X2),X3),X1) = implies(big_hat(X2,big_V(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_150,c_0_14]) ).
cnf(c_0_200,plain,
big_hat(not(implies(X1,X2)),big_V(X3,X1)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_201,plain,
implies(X1,implies(implies(big_V(X2,X1),X3),X2)) = implies(big_hat(X3,big_V(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_193,c_0_181]) ).
cnf(c_0_202,plain,
big_V(implies(X1,X2),implies(X3,not(X1))) = implies(X1,big_V(X2,not(X3))),
inference(rw,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_203,negated_conjecture,
big_hat(big_V(z,x),big_V(z,y)) != big_V(z,big_hat(x,y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_204,plain,
big_hat(big_V(X1,X2),big_V(X1,X3)) = big_V(X1,big_hat(X3,big_V(X1,X2))),
inference(spm,[status(thm)],[c_0_197,c_0_68]) ).
cnf(c_0_205,plain,
big_hat(big_V(X1,X2),big_V(X3,X1)) = big_V(X1,big_hat(X3,big_V(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_68]),c_0_14]) ).
cnf(c_0_206,plain,
big_hat(big_V(X1,X2),big_V(X2,X3)) = big_V(X2,big_hat(X3,big_V(X1,X2))),
inference(spm,[status(thm)],[c_0_197,c_0_106]) ).
cnf(c_0_207,plain,
implies(big_hat(X1,big_V(X2,X3)),X2) = implies(big_hat(X3,big_V(X1,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_110]),c_0_62]),c_0_199]),c_0_200]),c_0_62]),c_0_127]),c_0_201]) ).
cnf(c_0_208,plain,
implies(big_hat(X1,big_V(X2,X3)),X3) = implies(big_hat(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_62]),c_0_47]),c_0_49]),c_0_139]),c_0_150]),c_0_50]),c_0_62]) ).
cnf(c_0_209,negated_conjecture,
big_V(z,big_hat(y,big_V(z,x))) != big_V(z,big_hat(x,y)),
inference(rw,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_210,plain,
big_V(X1,big_hat(X2,big_V(X3,X1))) = big_V(X1,big_hat(X3,big_V(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_205]),c_0_206]) ).
cnf(c_0_211,plain,
implies(big_hat(X1,big_V(X2,X3)),X2) = implies(big_hat(X3,X1),X2),
inference(rw,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_212,negated_conjecture,
big_V(z,big_hat(x,big_V(z,y))) != big_V(z,big_hat(x,y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210]),c_0_14]) ).
cnf(c_0_213,plain,
big_V(X1,big_hat(X2,big_V(X1,X3))) = big_V(big_hat(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_211]),c_0_7]),c_0_14]) ).
cnf(c_0_214,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213]),c_0_74]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : LCL151-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n001.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 2400
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Oct 2 12:55:06 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.UDH4lbosi7/E---3.1_17827.p
% 278.27/37.14 # Version: 3.1pre001
% 278.27/37.14 # Preprocessing class: FSSSSMSSSSSNFFN.
% 278.27/37.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 278.27/37.14 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 278.27/37.14 # Starting new_bool_3 with 300s (1) cores
% 278.27/37.14 # Starting new_bool_1 with 300s (1) cores
% 278.27/37.14 # Starting sh5l with 300s (1) cores
% 278.27/37.14 # new_bool_3 with pid 17910 completed with status 0
% 278.27/37.14 # Result found by new_bool_3
% 278.27/37.14 # Preprocessing class: FSSSSMSSSSSNFFN.
% 278.27/37.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 278.27/37.14 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 278.27/37.14 # Starting new_bool_3 with 300s (1) cores
% 278.27/37.14 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 278.27/37.14 # Search class: FUUPM-FFSF21-MFFFFFNN
% 278.27/37.14 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 278.27/37.14 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 278.27/37.14 # H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 17914 completed with status 0
% 278.27/37.14 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 278.27/37.14 # Preprocessing class: FSSSSMSSSSSNFFN.
% 278.27/37.14 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 278.27/37.14 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 278.27/37.14 # Starting new_bool_3 with 300s (1) cores
% 278.27/37.14 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 278.27/37.14 # Search class: FUUPM-FFSF21-MFFFFFNN
% 278.27/37.14 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 278.27/37.14 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 278.27/37.14 # Preprocessing time : 0.001 s
% 278.27/37.14 # Presaturation interreduction done
% 278.27/37.14
% 278.27/37.14 # Proof found!
% 278.27/37.14 # SZS status Unsatisfiable
% 278.27/37.14 # SZS output start CNFRefutation
% See solution above
% 278.27/37.14 # Parsed axioms : 9
% 278.27/37.14 # Removed by relevancy pruning/SinE : 2
% 278.27/37.14 # Initial clauses : 7
% 278.27/37.14 # Removed in clause preprocessing : 0
% 278.27/37.14 # Initial clauses in saturation : 7
% 278.27/37.14 # Processed clauses : 38858
% 278.27/37.14 # ...of these trivial : 14302
% 278.27/37.14 # ...subsumed : 22030
% 278.27/37.14 # ...remaining for further processing : 2526
% 278.27/37.14 # Other redundant clauses eliminated : 0
% 278.27/37.14 # Clauses deleted for lack of memory : 0
% 278.27/37.14 # Backward-subsumed : 2
% 278.27/37.14 # Backward-rewritten : 1111
% 278.27/37.14 # Generated clauses : 3133275
% 278.27/37.14 # ...of the previous two non-redundant : 1449834
% 278.27/37.14 # ...aggressively subsumed : 0
% 278.27/37.14 # Contextual simplify-reflections : 0
% 278.27/37.14 # Paramodulations : 3133275
% 278.27/37.14 # Factorizations : 0
% 278.27/37.14 # NegExts : 0
% 278.27/37.14 # Equation resolutions : 0
% 278.27/37.14 # Total rewrite steps : 4679962
% 278.27/37.14 # Propositional unsat checks : 0
% 278.27/37.14 # Propositional check models : 0
% 278.27/37.14 # Propositional check unsatisfiable : 0
% 278.27/37.14 # Propositional clauses : 0
% 278.27/37.14 # Propositional clauses after purity: 0
% 278.27/37.14 # Propositional unsat core size : 0
% 278.27/37.14 # Propositional preprocessing time : 0.000
% 278.27/37.14 # Propositional encoding time : 0.000
% 278.27/37.14 # Propositional solver time : 0.000
% 278.27/37.14 # Success case prop preproc time : 0.000
% 278.27/37.14 # Success case prop encoding time : 0.000
% 278.27/37.14 # Success case prop solver time : 0.000
% 278.27/37.14 # Current number of processed clauses : 1406
% 278.27/37.14 # Positive orientable unit clauses : 1371
% 278.27/37.14 # Positive unorientable unit clauses: 35
% 278.27/37.14 # Negative unit clauses : 0
% 278.27/37.14 # Non-unit-clauses : 0
% 278.27/37.14 # Current number of unprocessed clauses: 1399973
% 278.27/37.14 # ...number of literals in the above : 1399973
% 278.27/37.14 # Current number of archived formulas : 0
% 278.27/37.14 # Current number of archived clauses : 1120
% 278.27/37.14 # Clause-clause subsumption calls (NU) : 0
% 278.27/37.14 # Rec. Clause-clause subsumption calls : 0
% 278.27/37.14 # Non-unit clause-clause subsumptions : 0
% 278.27/37.14 # Unit Clause-clause subsumption calls : 798
% 278.27/37.14 # Rewrite failures with RHS unbound : 0
% 278.27/37.14 # BW rewrite match attempts : 22224
% 278.27/37.14 # BW rewrite match successes : 3253
% 278.27/37.14 # Condensation attempts : 0
% 278.27/37.14 # Condensation successes : 0
% 278.27/37.14 # Termbank termtop insertions : 35669442
% 278.27/37.14
% 278.27/37.14 # -------------------------------------------------
% 278.27/37.14 # User time : 33.552 s
% 278.27/37.14 # System time : 1.165 s
% 278.27/37.14 # Total time : 34.717 s
% 278.27/37.14 # Maximum resident set size: 1616 pages
% 278.27/37.14
% 278.27/37.14 # -------------------------------------------------
% 278.27/37.14 # User time : 33.555 s
% 278.27/37.14 # System time : 1.167 s
% 278.27/37.14 # Total time : 34.722 s
% 278.27/37.14 # Maximum resident set size: 1676 pages
% 278.27/37.14 % E---3.1 exiting
% 278.27/37.14 % E---3.1 exiting
%------------------------------------------------------------------------------